Abstract
This paper is concerned with finite-time observer-based control of time-delay systems with one-sided Lipschitz nonlinearity and unknown energy-bounded exogenous disturbances. For this purpose, first, a robust sliding-mode observer is designed and the dynamical equations of the observer error are obtained. Then, the observer-based controller is designed to yield the finite-time boundedness of the time-delay closed-loop system and also satisfies the passivity performance index. By selecting the appropriate Lyapunov–Krasovskii functional, which is function of both systems states and observer error, the sufficient conditions are derived for robust finite-time boundedness of the closed-loop nonlinear one-sided Lipschitz system. In this regard, two theorems are given and the sufficient conditions are derived in terms of feasibility testing of the extracted linear matrix inequalities. Finally, computer simulations are performed to verify the theoretical achievements.
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